## Elements of Natural Philosophy, Part 1 |

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Page 10

Since the velocity in ABD is constant , all the lines OP , 00 , etc. , will be equal ( to

V ) , and therefore POS is a circle whose b B

acceleration at A is parallel to S the tangent at P , that is , is perpendicular to OP ,

i.e. to ...

Since the velocity in ABD is constant , all the lines OP , 00 , etc. , will be equal ( to

V ) , and therefore POS is a circle whose b B

**centre**is O. The direction ofacceleration at A is parallel to S the tangent at P , that is , is perpendicular to OP ,

i.e. to ...

Page 11

... and the acceleration is directed to or from the

instant ( $$ 66 , 78 ) . ( c ) If the components of the velocity parallel to each axis

be equimultiples of the distances from the other axis , the path is a straight line

passing ...

... and the acceleration is directed to or from the

**centre**of the curve at everyinstant ( $$ 66 , 78 ) . ( c ) If the components of the velocity parallel to each axis

be equimultiples of the distances from the other axis , the path is a straight line

passing ...

Page 15

Bi we may also prove this important proposition as follows : Let A be the

the circle , and the hodographic origin . Join OA and draw the perpendiculars PM

to OA and ON to PA . Then OP is the velocity in the orbit : and ON , being ...

Bi we may also prove this important proposition as follows : Let A be the

**centre**ofthe circle , and the hodographic origin . Join OA and draw the perpendiculars PM

to OA and ON to PA . Then OP is the velocity in the orbit : and ON , being ...

Page 16

The usual unit angle is ( as explained in treatises on plane trigonometry ) that

which subtends at the

radius ; being an angle of = 57 ° 29578 ... = 57 ° 17'44 " : 8 nearly . 56. The

angular ...

The usual unit angle is ( as explained in treatises on plane trigonometry ) that

which subtends at the

**centre**of a circle an arc whose length is equal 180 ° to theradius ; being an angle of = 57 ° 29578 ... = 57 ° 17'44 " : 8 nearly . 56. The

angular ...

Page 22

From A as

CB touching this circle represents the most deviated resultant . Hence CBA is a

right angle ; A and AB sin BCA = СА . 77. A most interesting application of this

case ...

From A as

**centre**, with AB the less halfamplitude as radius , describe a circle .CB touching this circle represents the most deviated resultant . Hence CBA is a

right angle ; A and AB sin BCA = СА . 77. A most interesting application of this

case ...

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acceleration according acting action amount angle angular applied attraction axes axis body called centre centre of inertia circle component condition consider constant corresponding couple course curvature curve denote density described determined direction displacement distance divided effect elastic elements energy equal equations equilibrium evidently experience expression figure fixed fluid force friction give given gravity harmonic Hence important increase infinitely small instant interval kinetic length less mass matter mean measured method motion moving natural normal observation opposite parallel particle passing path perpendicular plane portion position potential practical pressure principle problem produce projection proportional quantity radius reference relative remain respectively rest resultant right angles rigid rotation round sides simple solid space spherical square straight strain stress suppose surface theory turned uniform unit velocity weight whole wire